Measurement Scales

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Measurement scales are the mappings used for representing the empirical relation system. It is mainly of 5 types −

  • Nominal Scale
  • Ordinal Scale
  • Interval Scale
  • Ratio Scale
  • Absolute Scale

Nominal Scale

It places the elements in a classification scheme. The classes will not be ordered. Each and every entity should be placed in a particular class or category based on the value of the attribute.

It has two major characteristics −

  • The empirical relation system consists only of different classes; there is no notion of ordering among the classes.

  • Any distinct numbering or symbolic representation of the classes is an acceptable measure, but there is no notion of magnitude associated with the numbers or symbols.

Ordinal Scale

It places the elements in an ordered classification scheme. It has the following characteristics −

  • The empirical relation system consists of classes that are ordered with respect to the attribute.

  • Any mapping that preserves the ordering is acceptable.

  • The numbers represent ranking only. Hence, addition, subtraction, and other arithmetic operations have no meaning.

Interval Scale

This scale captures the information about the size of the intervals that separate the classification. Hence, it is more powerful than the nominal scale and the ordinal scale.

It has the following characteristics −

  • It preserves order like the ordinal scale.

  • It preserves the differences but not the ratio.

  • Addition and subtraction can be performed on this scale but not multiplication or division.

If an attribute is measurable on an interval scale, and M and M’ are mappings that satisfy the representation condition, then we can always find two numbers a and b such that,

M = aM’ + b

Ratio Scale

This is the most useful scale of measurement. Here, an empirical relation exists to capture ratios. It has the following characteristics −

  • It is a measurement mapping that preserves ordering, the size of intervals between the entities and the ratio between the entities.

  • There is a zero element, representing total lack of the attributes.

  • The measurement mapping must start at zero and increase at equal intervals, known as units.

  • All arithmetic operations can be applied.

Here, mapping will be of the form

M = aM’

Where ‘a’ is a positive scalar.

Absolute Scale

On this scale, there will be only one possible measure for an attribute. Hence, the only possible transformation will be the identity transformation.

It has the following characteristics −

  • The measurement is made by counting the number of elements in the entity set.

  • The attribute always takes the form “number of occurrences of x in the entity”.

  • There is only one possible measurement mapping, namely the actual count.

  • All arithmetic operations can be performed on the resulting count.

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